Leibniz algebra deformations of a Lie algebra

2008/02/09 by Alice Fialowski, Ashis Mandal · 3 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology #math.KT #math.QA #msc:13D03 #msc:13D10 #msc:14D15

paper · pdf · doi:10.1063/1.2981562

15 pages

arxiv created 2008/02/09 · openalex publication_date 2008/09/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this note we compute Leibniz algebra deformations of the three-dimensional Heisenberg Lie algebra n3 and compare it to its Lie deformations. It turns out that there are three extra Leibniz deformations. We also describe a versal Leibniz deformation of n3 with the versal base.

Citations

• Universal enveloping algebras of Leibniz algebras and (co)homology

Cited by

• Topics on n-ary algebras
• On a class of n-Leibniz deformations of the simple Filippov algebras
• Deformations of the five dimensional Heisenberg Lie algebra

Related

• An Example of Constructing Versal Deformation for Leibniz Algebras
• About Leibniz cohomology and deformations of Lie algebras
• Versal Deformations of Three Dimensional Lie Algebras as L-infinity Algebras
• The Moduli Space of Three Dimensional Lie Algebras
• Versal deformations of Leibniz algebras